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-   -   Subproject #11: 2^2 * 3 - Lose the '3' (https://www.mersenneforum.org/showthread.php?t=16075)

 schickel 2011-09-22 10:47

Subproject #11: 2^2 * 3 - Lose the '3'

This is a project suggested by 10metreh. He hopes we can achieve some terminations with this project.

The hope is that a sequence that currently has 2^2 * 3 as a guide will lose the 3, if the remaining composite factors "properly".

I pulled a status on these sequences right before posting but, as always, check the status of a sequence in the DB before starting any significant work....

[Note: Due to the sheer number of sequences that are currently 2^2 * 3, this message has been split....]

Sequences:[code]894702 1071. sz 112 2^2 * 3 * 11
668922 1469. sz 112 2^2 * 3 * 5
800010 1351. sz 112 2^2 * 3 * 5
596808 1007. sz 112 2^2 * 3 * 5
867228 1034. sz 112 2^2 * 3^2
638680 833. sz 112 2^2 * 3^2
738240 1698. sz 112 2^2 * 3^2 * 17
844758 1712. sz 112 2^2 * 3^2 * 5
630024 2457. sz 112 2^2 * 3^2 * 7 * 89459 * 138072719
293136 989. sz 113 2^2 * 3
369978 1188. sz 113 2^2 * 3
642000 1705. sz 113 2^2 * 3 * 1669
526752 618. sz 113 2^2 * 3 * 17
244872 844. sz 113 2^2 * 3 * 2437094789966273
966180 1880. sz 113 2^2 * 3 * 29
832314 2263. sz 113 2^2 * 3 * 5
932070 1072. sz 113 2^2 * 3 * 5
872784 1104. sz 113 2^2 * 3 * 5 * 11
746880 538. sz 113 2^2 * 3 * 5 * 11
734088 1169. sz 113 2^2 * 3 * 5^2
823116 1414. sz 113 2^2 * 3 * 53
665478 757. sz 113 2^2 * 3 * 577
592506 1114. sz 113 2^2 * 3 * 79
836694 894. sz 113 2^2 * 3^2 * 29
992970 999. sz 113 2^2 * 3^2 * 37
681500 1255. sz 113 2^2 * 3^2 * 5
704850 1590. sz 113 2^2 * 3^2 * 71
227200 781. sz 113 2^2 * 3^3
682380 1726. sz 113 2^2 * 3^3
777762 1384. sz 113 2^2 * 3^3
493992 1754. sz 113 2^2 * 3^3 * 5
385176 1097. sz 113 2^2 * 3^3 * 5
968484 970. sz 114 2^2 * 3
962232 828. sz 114 2^2 * 3
933240 1082. sz 114 2^2 * 3
891702 1122. sz 114 2^2 * 3
769068 1128. sz 114 2^2 * 3
601824 2081. sz 114 2^2 * 3
533160 1064. sz 114 2^2 * 3
564870 772. sz 114 2^2 * 3
239778 1486. sz 114 2^2 * 3
358506 1062. sz 114 2^2 * 3
656616 2093. sz 114 2^2 * 3 * 1097
106080 873. sz 114 2^2 * 3 * 137
559548 1250. sz 114 2^2 * 3 * 17 * 75883
699588 1280. sz 114 2^2 * 3 * 181
517392 878. sz 114 2^2 * 3 * 1823
323964 1940. sz 114 2^2 * 3 * 19
377160 1123. sz 114 2^2 * 3 * 281
946728 1014. sz 114 2^2 * 3 * 29
515220 1546. sz 114 2^2 * 3 * 317
712824 899. sz 114 2^2 * 3 * 3313
596032 546. sz 114 2^2 * 3 * 467 * 3582899
202776 1403. sz 114 2^2 * 3 * 47
384606 2109. sz 114 2^2 * 3 * 5
803616 1068. sz 114 2^2 * 3 * 5 * 103
425052 1059. sz 114 2^2 * 3 * 5 * 11
865032 1739. sz 114 2^2 * 3 * 5 * 13 * 37
870072 1052. sz 114 2^2 * 3 * 5 * 173 * 203989
871470 904. sz 114 2^2 * 3 * 5 * 19
863370 494. sz 114 2^2 * 3 * 5 * 383 * 9293 * 48673
429072 1087. sz 114 2^2 * 3 * 5^2 * 11
357408 1233. sz 114 2^2 * 3 * 5^3
960900 1599. sz 114 2^2 * 3 * 53
450570 2498. sz 114 2^2 * 3 * 543734960947
380610 2199. sz 114 2^2 * 3 * 607
636024 965. sz 114 2^2 * 3 * 71
556920 1027. sz 114 2^2 * 3 * 727
666384 978. sz 114 2^2 * 3^2
573648 530. sz 114 2^2 * 3^2
993438 510. sz 114 2^2 * 3^2 * 11 * 13
652296 1544. sz 114 2^2 * 3^2 * 11 * 19
940224 1739. sz 114 2^2 * 3^2 * 479
967024 1144. sz 114 2^2 * 3^2 * 5 * 17
779892 779. sz 114 2^2 * 3^3
933870 685. sz 114 2^2 * 3^3
442344 1132. sz 114 2^2 * 3^3
856548 1112. sz 114 2^2 * 3^3 * 11 * 37
582144 1095. sz 114 2^2 * 3^3 * 37
922158 1305. sz 115 2^2 * 3
862866 646. sz 115 2^2 * 3
274272 985. sz 115 2^2 * 3 * 283
894066 1194. sz 115 2^2 * 3 * 31 * 24373
192360 963. sz 115 2^2 * 3 * 37 * 53^2
680544 1275. sz 115 2^2 * 3 * 373
788106 1476. sz 115 2^2 * 3 * 439
377688 2005. sz 115 2^2 * 3 * 5
641520 934. sz 115 2^2 * 3 * 5 * 617
915384 1102. sz 115 2^2 * 3 * 79
216390 920. sz 115 2^2 * 3^2
269208 1199. sz 115 2^2 * 3^4 * 43
303756 2519. sz 116 2^2 * 3
749832 680. sz 116 2^2 * 3
865164 1065. sz 116 2^2 * 3
844536 1279. sz 116 2^2 * 3
687336 1137. sz 116 2^2 * 3
487656 2478. sz 116 2^2 * 3
475668 907. sz 116 2^2 * 3 * 11 * 1637
126756 1184. sz 116 2^2 * 3 * 11 * 433
287304 1485. sz 116 2^2 * 3 * 127
214728 1292. sz 116 2^2 * 3 * 13
394680 2382. sz 116 2^2 * 3 * 149 * 8712059
941850 2111. sz 116 2^2 * 3 * 17
270504 1912. sz 116 2^2 * 3 * 173
466656 799. sz 116 2^2 * 3 * 19 * 89
983328 1614. sz 116 2^2 * 3 * 239
492688 2368. sz 116 2^2 * 3 * 2591
333300 1237. sz 116 2^2 * 3 * 38923
863640 1048. sz 116 2^2 * 3 * 3943
929880 1075. sz 116 2^2 * 3 * 41
215088 912. sz 116 2^2 * 3 * 4421
950280 1250. sz 116 2^2 * 3 * 5
624798 1728. sz 116 2^2 * 3 * 5
746564 871. sz 116 2^2 * 3 * 5
478440 978. sz 116 2^2 * 3 * 5 * 47
443370 1530. sz 116 2^2 * 3 * 5 * 97 * 197
448476 851. sz 116 2^2 * 3 * 5^2 * 25121
376992 672. sz 116 2^2 * 3 * 59
758322 2239. sz 116 2^2 * 3 * 59 * 271
840012 1918. sz 116 2^2 * 3 * 709
426072 2703. sz 116 2^2 * 3 * 73 * 1151
324072 1027. sz 116 2^2 * 3^2
664356 2924. sz 116 2^2 * 3^2
407736 586. sz 116 2^2 * 3^2
180108 751. sz 116 2^2 * 3^2
103782 851. sz 116 2^2 * 3^2 * 11
850164 2307. sz 116 2^2 * 3^2 * 11 * 1289
967680 2008. sz 116 2^2 * 3^2 * 1571
582750 1396. sz 116 2^2 * 3^2 * 17 * 19
346200 1908. sz 116 2^2 * 3^2 * 17 * 29
421428 951. sz 116 2^2 * 3^2 * 2617
143676 1430. sz 116 2^2 * 3^2 * 283
296904 902. sz 116 2^2 * 3^2 * 37
183042 758. sz 116 2^2 * 3^2 * 467
649944 1514. sz 116 2^2 * 3^2 * 5
674912 407. sz 116 2^2 * 3^2 * 5
561000 2208. sz 116 2^2 * 3^2 * 5 * 13
190620 1468. sz 116 2^2 * 3^2 * 5^3 * 3408058099731294299
918054 835. sz 116 2^2 * 3^2 * 61
778300 1004. sz 116 2^2 * 3^2 * 991
338250 2866. sz 116 2^2 * 3^3
171462 1162. sz 116 2^2 * 3^3 * 115133
652386 1993. sz 116 2^2 * 3^3 * 13
971280 1235. sz 116 2^2 * 3^4
760000 832. sz 116 2^2 * 3^4 * 151
722142 1099. sz 116 2^2 * 3^5 * 11
834312 1311. sz 117 2^2 * 3
338040 1463. sz 117 2^2 * 3
711800 1277. sz 117 2^2 * 3 * 1073491
346980 2708. sz 117 2^2 * 3 * 1087
834756 645. sz 117 2^2 * 3 * 11 * 13 * 41
273552 898. sz 117 2^2 * 3 * 19 * 37 * 269
652068 1160. sz 117 2^2 * 3 * 23 * 853
245274 1424. sz 117 2^2 * 3 * 23333
852264 1187. sz 117 2^2 * 3 * 281
435504 702. sz 117 2^2 * 3 * 29 * 443
118230 1680. sz 117 2^2 * 3 * 333271
228228 1231. sz 117 2^2 * 3 * 3347
125016 980. sz 117 2^2 * 3 * 35839
288144 1343. sz 117 2^2 * 3 * 37 * 1393326973 * 13825514861
710610 1215. sz 117 2^2 * 3 * 41
441450 1068. sz 117 2^2 * 3 * 5
[/code][B]Last complete status update: [COLOR=blue]2012-Jun-08[/COLOR][/B]

[SIZE=1]PS. Check below for some discussion about what it takes to lose the 3.[/SIZE]

 Mini-Geek 2011-09-22 23:10

[Old message at the bottom...:grin:][code]
112350 2272. sz 117 2^2 * 3 * 5 * 11 * 71
594288 1962. sz 117 2^2 * 3 * 5 * 19 * 23 * 137
408408 576. sz 117 2^2 * 3 * 5 * 20297
997944 2058. sz 117 2^2 * 3 * 5 * 229
799512 421. sz 117 2^2 * 3 * 5 * 59 * 1409
516588 1126. sz 117 2^2 * 3 * 5 * 593 * 12176539883962932799
753372 1284. sz 117 2^2 * 3 * 61
313704 573. sz 117 2^2 * 3 * 853999 * 2705291
958056 647. sz 117 2^2 * 3^2
357792 1206. sz 117 2^2 * 3^2 * 111491
193320 986. sz 117 2^2 * 3^2 * 17
139056 2251. sz 117 2^2 * 3^2 * 44533
427704 1480. sz 117 2^2 * 3^2 * 5
559368 1873. sz 117 2^2 * 3^2 * 5 * 173
392340 1906. sz 117 2^2 * 3^2 * 5^4
477084 707. sz 117 2^2 * 3^3 * 19
574344 797. sz 117 2^2 * 3^3 * 5 * 103561
197310 1125. sz 117 2^2 * 3^3 * 5 * 2671
781302 2328. sz 117 2^2 * 3^3 * 5 * 9619
619800 1502. sz 117 2^2 * 3^4 * 5
353520 1009. sz 118 2^2 * 3
786720 977. sz 118 2^2 * 3
578760 1618. sz 118 2^2 * 3 * 101 * 110647 * 722321737
509832 1739. sz 118 2^2 * 3 * 31 * 42257
136192 622. sz 118 2^2 * 3 * 5 * 103
878752 1562. sz 118 2^2 * 3 * 5 * 7^2
893670 1174. sz 118 2^2 * 3 * 5146289
251580 1474. sz 118 2^2 * 3 * 67
233304 818. sz 118 2^2 * 3^2
927468 1292. sz 118 2^2 * 3^2
111426 1149. sz 118 2^2 * 3^2 * 11 * 13 * 6779
316960 1131. sz 118 2^2 * 3^2 * 29 * 467
768612 1943. sz 118 2^2 * 3^2 * 383 * 1933
547200 1441. sz 118 2^2 * 3^2 * 39317
708930 1343. sz 118 2^2 * 3^2 * 39461 * 7660223
474580 2321. sz 118 2^2 * 3^2 * 5 * 2377
799200 918. sz 118 2^2 * 3^2 * 5 * 71 * 1949
914760 2157. sz 118 2^2 * 3^2 * 5039
116040 1362. sz 118 2^2 * 3^3 * 19 * 29^2 * 53 * 1287989
922752 803. sz 118 2^2 * 3^3 * 5 * 13 * 47
753522 1597. sz 118 2^2 * 3^3 * 5 * 23 * 1223
531024 2662. sz 118 2^2 * 3^4 * 23
293496 857. sz 118 2^2 * 3^4 * 5
873528 561. sz 119 2^2 * 3 * 103
766560 1681. sz 119 2^2 * 3 * 11 * 17 * 47 * 331
787620 636. sz 119 2^2 * 3 * 19^2 * 71 * 2333
935008 1907. sz 119 2^2 * 3 * 2514737
533904 946. sz 119 2^2 * 3 * 41 * 769
394200 1372. sz 119 2^2 * 3 * 5^2 * 19
269688 2920. sz 119 2^2 * 3^2 * 13 * 71
838602 983. sz 120 2^2 * 3
643530 911. sz 120 2^2 * 3 * 1064685151
479136 2773. sz 120 2^2 * 3 * 11
558120 3407. sz 120 2^2 * 3 * 23 * 79
467016 4034. sz 120 2^2 * 3 * 281
557490 1239. sz 120 2^2 * 3 * 5
252588 1589. sz 120 2^2 * 3 * 5 * 103 * 2693 * 4856055876957941
308610 2389. sz 120 2^2 * 3 * 5 * 11 * 467
853740 551. sz 120 2^2 * 3 * 5 * 43
657816 1422. sz 120 2^2 * 3 * 653
277956 731. sz 120 2^2 * 3 * 7 * 13 * 643 * 6733
875520 1643. sz 120 2^2 * 3 * 7 * 71 * 257 * 997 * 6337
404868 1149. sz 120 2^2 * 3 * 800221
400158 1737. sz 120 2^2 * 3 * 911124659
623190 1551. sz 120 2^2 * 3^2 * 19 * 67
402780 439. sz 121 2^2 * 3
267102 654. sz 121 2^2 * 3 * 137
972720 1390. sz 121 2^2 * 3 * 1877 * 122029 * 504485371877
337008 592. sz 121 2^2 * 3 * 19 * 43
350994 959. sz 121 2^2 * 3 * 39610189
334548 809. sz 121 2^2 * 3 * 5 * 157
344136 889. sz 121 2^2 * 3^2
693812 1094. sz 121 2^2 * 3^2 * 19 * 77291
378642 1295. sz 121 2^2 * 3^2 * 5
227160 1294. sz 121 2^2 * 3^2 * 661
342216 1646. sz 121 2^2 * 3^5 * 2687
894456 441. sz 122 2^2 * 3 * 11
515064 1728. sz 122 2^2 * 3 * 11357029
201048 695. sz 122 2^2 * 3 * 13 * 412967
236840 722. sz 122 2^2 * 3 * 19
315780 405. sz 122 2^2 * 3 * 47 * 16573
438462 419. sz 122 2^2 * 3 * 5
230520 414. sz 122 2^2 * 3 * 5 * 29
716130 1911. sz 122 2^2 * 3 * 8200463933
448224 729. sz 122 2^2 * 3^2
497928 3332. sz 122 2^2 * 3^2
79584 1451. sz 122 2^2 * 3^2 * 11 * 23
981960 512. sz 122 2^2 * 3^2 * 12497 * 843811
662850 3663. sz 122 2^2 * 3^2 * 13
175602 561. sz 122 2^2 * 3^3 * 41 * 313 * 3187 * 6353 * 11117 * 201511
122508 1838. sz 122 2^2 * 3^3 * 5009
911484 401. sz 123 2^2 * 3 * 10037
178002 2070. sz 123 2^2 * 3^3 * 5
61116 1655. sz 124 2^2 * 3
767520 4433. sz 124 2^2 * 3 * 11 * 151
827880 1228. sz 124 2^2 * 3^2
985080 410. sz 125 2^2 * 3
494808 716. sz 125 2^2 * 3
919386 1065. sz 125 2^2 * 3 * 11
469812 3179. sz 125 2^2 * 3 * 1231
904188 2830. sz 125 2^2 * 3 * 17 * 107 * 9109
363126 1579. sz 125 2^2 * 3 * 19
938250 1967. sz 125 2^2 * 3 * 5 * 1013 * 30941
122688 1477. sz 125 2^2 * 3 * 5 * 181 * 300721
523044 1529. sz 125 2^2 * 3 * 5 * 58481 * 41557478047
462168 928. sz 125 2^2 * 3 * 5 * 59
795912 2455. sz 125 2^2 * 3 * 5 * 7 * 19^2 * 89 * 397
761516 1447. sz 125 2^2 * 3 * 5^2 * 11 * 673
996252 1758. sz 125 2^2 * 3 * 578861
336990 1354. sz 125 2^2 * 3^2 * 11 * 31019
980784 1188. sz 125 2^2 * 3^2 * 149 * 8218961
159846 857. sz 125 2^2 * 3^2 * 17 * 53 * 271 * 3529
170748 1565. sz 125 2^2 * 3^2 * 5 * 7 * 41 * 43 * 317 * 373
836244 1762. sz 125 2^2 * 3^2 * 7 * 31 * 2905087 * 3354133
116688 1237. sz 125 2^2 * 3^3
917790 2507. sz 125 2^2 * 3^3 * 5 * 7 * 342521
530640 3465. sz 126 2^2 * 3 * 149670900061
228150 881. sz 126 2^2 * 3^2 * 5 * 175753
509928 4524. sz 127 2^2 * 3
168912 2014. sz 127 2^2 * 3 * 47 * 2311
837480 1466. sz 127 2^2 * 3 * 47 * 6113 * 431567
511440 719. sz 127 2^2 * 3 * 5 * 89
161064 1786. sz 128 2^2 * 3 * 17 * 577
158814 3458. sz 130 2^2 * 3 * 17 * 3529
794184 1820. sz 130 2^2 * 3 * 5360837011597
129336 1923. sz 130 2^2 * 3^2 * 29 * 7949
102360 430. sz 130 2^2 * 3^3 * 109 * 131 * 194463079493
181650 1951. sz 131 2^2 * 3
259704 4605. sz 132 2^2 * 3 * 16607 * 22532987
381510 916. sz 132 2^2 * 3^2 * 5 * 683 * 737766131
643760 1373. sz 134 2^2 * 3 * 29^2 * 251
805686 472. sz 134 2^2 * 3 * 41
854418 404. sz 134 2^2 * 3 * 67 * 251 * 2809691
223692 1359. sz 135 2^2 * 3^2 * 491
715776 1941. sz 136 2^2 * 3 * 11 * 13 * 19
20076 3403. sz 136 2^2 * 3 * 50828150957
38880 1139. sz 138 2^2 * 3
425280 665. sz 138 2^2 * 3 * 61 * 787 * 82781
84054 1099. sz 139 2^2 * 3 * 5
128136 499. sz 139 2^2 * 3 * 5 * 118860961
52374 2535. sz 139 2^2 * 3^3 * 5
56928 1003. sz 140 2^2 * 3 * 17 * 766169
611156 5703. sz 144 2^2 * 3^2 * 167 * 6047 * 7451
998088 1304. sz 145 2^2 * 3^2
39060 1123. sz 147 2^2 * 3 * 17 * 29
940050 1624. sz 152 2^2 * 3^3 * 1163
890460 898. sz 156 2^2 * 3 * 53 * 103
[/code][B][COLOR=blue]Last complete update: 2012-Jun-08[/COLOR][/B]

Reserving 199710.
Are we deleting once reserved, or adding a reservation tag? For now, I'll add a reservation tag, as it's easier to delete than to recover the info.

 schickel 2011-09-23 02:30

[QUOTE=Mini-Geek;272453]Reserving 199710.
Are we deleting once reserved, or adding a reservation tag? For now, I'll add a reservation tag, as it's easier to delete than to recover the info.[/QUOTE]That'll work for now. We'll have to see how the project goes....

 RobertS 2011-09-23 10:34

Reserving 321660

 Mini-Geek 2011-09-23 11:25

[QUOTE=schickel;272376][SIZE="1"]PS. Clifford has mentioned the required form for a factorization to result in losing the 3, but I'm haven't been able to find that email yet....[/SIZE][/QUOTE]

On this sort of subject: My driver has become 2^2 * 3^3. Is this significantly worse to get out of than 2^2 * 3? I'm wondering if that's why only 2^2 * 3^1 is listed.

 10metreh 2011-09-23 15:40

[QUOTE=Mini-Geek;272503]On this sort of subject: My driver has become 2^2 * 3^3. Is this significantly worse to get out of than 2^2 * 3? I'm wondering if that's why only 2^2 * 3^1 is listed.[/QUOTE]

I think it has the same conditions; it isn't included because we don't the top post to become huge.

 schickel 2011-09-23 21:46

[QUOTE=10metreh;272528]I think it has the same conditions; it isn't included because we don't the top post to become huge.[/QUOTE]A quick count shows that there are >600 sequences with some combination of 2^2 * 3, either alone or with other factors, but without a 7.

This is the highest power of 3 right now:[code]940224 1734. sz 113 2^2 * 3^9[/code]For those following along at home, I'll post an updated status file on everything open later this afternoon.....

 Batalov 2011-09-23 23:02

I'll take 611156 (i4327), 960096 (i2655) and 378756 (i2911).

 Mini-Geek 2011-09-24 02:59

Escape from 2^2*3 to 2^2 successful at 118 digits! :smile:
[url]http://factordb.com/sequences.php?se=1&aq=199710[/url]
It's now on a slow downward-ish slide, hopefully it will become the downdriver!

 Batalov 2011-09-24 03:32

Don't forget - 3 comes and goes... See [URL="http://www.factordb.com/sequences.php?se=1&eff=2&aq=611156&action=range&fr=4310&to=4350"]for example[/URL] 611156.

 schickel 2011-09-24 03:40

[QUOTE=schickel;272548]For those following along at home, I'll post an updated status file on everything open later this afternoon.....[/QUOTE]As promised, [URL="ftp://ftp.frontiernet.net/pub/users/aliquot/AllSeq.zip"]here[/URL] is a current status file for everything.....I left it sorted by sequence this time.

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